How’s that title for clickbait, hey?

Perhaps you’ve spent some time in the corners of the internet that argue about whether the times tables should be included in school mathematics curricula. If so, you understand the emotions associated with the role of memory in mathematics education, and I think you may be in a perfect spot.

To better situate my claim, allow me to restate the title a touch more precisely:

Retrieving a fact from memory is not a mathematical act

Let me clarify that retrieving a fact from memory may not be a mathematical act, but it is a fascinating act. It is also an important and useful cognitive act, worthy of awe and investigation. It’s just not a uniquely mathematical act.

As the years of classroom teaching have gone along, this statement has been illustrated time and time again; However, a particularly potent example occurred recently, and, after months of it weighing on my mathematical memory, I decided to catalogue it here.

Consider the following task:

A few minutes after I launched the task, I approached a table of three pre-service teachers working together and engaged in the following exchange:

Me: There’s lots here. Can I ask which shape you started with?

Student: We started with the purple square is 2.

Me: Oh perfect. You are confident it’s 2? How are you sure?

Student: I’ve done this exact problem before and I remembered it was 2.

With respect to the value of the purple square: Did she do mathematics?

I say no. She remembered a number.

Now, numbers are mathematical objects, but she did not engage in a mathematical act to arrive at the conclusion that the purple square was 2.

Time for two important clarifications:

We, as humans, are capable of memorizing mathematical facts through both mathematical and non-mathematical acts, so this particular result may have been the result of previous mathematical acts—but that is not a guarantee.

We might interpret her act of retrieving the value of the purple square in that moment as a learning act in the sense that, through retrieval, she strengthened her ability to retrieve it once again. Through the act of retrieval, she engaged in structural change.

For me, mathematical acts make and/or maintain mathematical meaning—they build understanding and coordinate sense.

Memory retrieval plays a role (namely, in fostering retention of concepts and in lessening the burden of moving meaning making forward in the moment), but they, in and of themselves, are not mathematical acts. Recalling the result of a previous experience provides no evidence of her mathematical maintenance or coordination of meaning in that moment.

Experiences like this always beg three questions from me as a classroom teacher widely interested in the teaching and learning of mathematics:

What opportunities am I giving my students to engage in mathematical acts?

What counts as evidence of mathematical activity in my classroom?

Are there moments when acts of memory are masquerading as acts of mathematics?

NatBanting